If the concrete patio behind your house is plain or boring, and you want to replace it with flagstone or some other stone, you don't necessarily need to remove the old concrete. The process of laying a stone patio involves a base layer of cement anyway, and you've already got that in place. If the patio is in good structural shape, there's no reason you can't lay right over it with the stone, by just adding a little extra cement. Misting it as it dries, ensures strong, solid finished joints.
Sweep off the patio. Hose down the surface very well. Scrub it down with additional water and dish soap, getting a good lather. Scrub it free of all dirt, grime, moss and anything else that might interfere with the performance of the cement. Rinse it thoroughly. Let it dry completely.
Lay out your stones, placing all of them exactly where you want them to be on the patio. Put between 1/2 inch and 3/4 inches of space between them. If cuts are necessary at the edges, make them with your masonry saw.
Mix your cement in the wheelbarrow with your shovel. Starting at one corner, lift up one of the stones and, with your cement trowel, cake the back of it with about half an inch of cement. Spread another half an inch of cement on the concrete patio, in the spot where you lifted the stone. Press the stone back into place. Press just firmly enough that cement starts to come up the sides.
Repeat the process for each stone on the patio. For each group of four or five stones that you lay, trowel additional cement into the spaces between them, smoothing it out at the top and scooping any stray cement off the surface of the stone. Continue until all the stones have been cemented down and all the spaces between them are filled with cement.
Mist the entire patio with your garden hose. Let it dry overnight. Mist it again in the morning and at night, for the next two days. When it dries on the third day, it's ready for use.